Standard Form Calculator

Use this calculator to easily convert a number in standard form (a.k.a. scientific notation, a.k.a. engineering notation). Write a large number or a decimal with a many digits past the decimal point in standard form.

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1. What is the standard form of a number?
2. Writing a number in standard form

What is the standard form of a number?

The standard form is also called E-notation, scientific form of a number, or standard index form. It is a way of expressing numbers deemed too large or too small to be conveniently written in the more familiar decimal form. Many calculators support scientific mode for working with such numbers. Even though it is less necessary now than in times before personal computing, the standard form remains popular among engineers, scientists and mathematicians, as well as students in these disciplines.

The form of a number in standard notation is m x 10 n which reads "m times 10 raised to the power of n". The exponent n is always an integer (whole number) while the coefficient m (mantissa, significand) can be any real number. The most convenient form (normalized notation) is one in which the exponent is chosen in such a way that the coefficient is between 1 and 9. The sign of the number is written the usual way - with a plus or minus before it.

Writing numbers in standard form makes it easier to compare orders-of-magnitude. For example, the mass of a proton is 0.000 000 000 000 000 000 000 001 6726 g and the mass of an electron is 0.000 000 000 000 000 000 000 000 000 910 938 356 g. It is hard to compare the two this way, but when we write them as 1.6726 x 10 -24 and 9.109 383 56 x 10 -28 we can just compare the exponents, and since -24 is larger than -28, the proton is about 4 orders of magnitude (10,000 times) more massive than the electron.

Writing a number in standard form

It should be noted that converting decimal numbers to standard form numbers does not change the value of the number, it just changes its form, as suggested by the name. Using our standard form calculator, you can do the conversion quickly and easily, however if you want to do it by hand, here is the algorithm for doing so.

1. Move the decimal point enough places so that the number becomes smaller than 10, but larger than 1.
2. If you moved the decimal point to the left, append "x 10 n " to the number, where n is the number of positions you moved the point. If you moved it to the right, append "x 10 -n ", using the same logic.

For example, let us write the number 12,340,000 in normalized standard form. First, we move the decimal point 7 positions to the left so the number becomes 1.2340000. We can drop the zeroes in most scenarios (unless we want to keep them as significant digits to indicate precision) so, after adding x 10 7 we can write it down as 1.234 x 10 7 in scientific notation and 1.055e7 or 1.055e+7 in e notation. Both types of notations are supplied when using our online tool.